On certain families of naturally graded Lie algebras

2000/10/23 by Jose Maria Ancochea, Ancochea, Jose Maria, Otto Rutwig Campoamor +1
Mathematics · #17B30 #17B56 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B30 #msc:17B56

paper · pdf · doi:10.48550/arxiv.math/0010216

30 pages, 2 tables

arxiv created 2000/10/23 · arxiv updated 2009/11/30

Abstract

In this work large families of naturally graded nilpotent Lie algebras in arbitrary dimension and characteristic sequence (n,q,1), with n odd, satisfying the centralizer property, are given. This condtion constitutes a generalization, for a nilpotent Lie agebra, of the structural properties charactrizing the Lie algebra Q_n. By considering certain cohomological classes of the space H²(\frakg,ℂ), it is shown that, with few exceptions, the isomorphism classses of these algebras are given by central extensions of Q_n by ℂ^p which preserve the nilindex and the natural graduation.

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